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arXiv:2511.21079 · Physical Review A

Witness wedges in fidelity-deviation plane: separating teleportation advantage and Bell-inequality violation

Kyoungho Cho, Jeongho Bang

quant-phSubmitted Nov 26, 2025• Announced Nov 27, 2025• 0 citations
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Abstract

We develop a unified framework to analyze $d$-dimensional quantum teleportation through the joint geometry of two complementary figures of merit: average fidelity $F$ (how well a protocol works on average) and fidelity deviation $D$ (how uniformly it works across the inputs). Technically, we formulate a representation-theoretical framework based on Schur-Weyl duality and permutation symmetry calculus that reduce the higher-moment Haar averages to a finite set of trace invariants of the composed correction unitaries. This yields closed-form expressions for $F$ and $D$ in arbitrary Hilbert-space dimension and delivers tight bounds that link the admissible deviation directly to the gap from the optimal average performance. In particular, any measured pair $(F, D)$ can be ported into a visibility estimate for isotropic channel resources, turning the $(F, D)$-plane into a calibrated diagnostic map. We further cast the teleportation advantage and CGLMP-inequality violation as two witnesses lines in the $(F,D)$ plane: one line certifies that $F$ beats the classical benchmark $2/(d{+}1)$, while the other line certifies the Bell nonlocality. Their identical slope but distinct intercepts expose a quantitative gap between "entangled yet local" and "genuinely nonlocal" resources.

Journal reference
Physical Review A, 113, 052458 (2026)
DOI
10.1103/q9d2-5zv4
Comments
16 pages

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We develop a unified framework to analyze ddd-dimensional quantum teleportation through the joint geometry of two complementary figures of merit: average fidelity FFF (how well a protocol works on average) and fidelity deviation DDD (how uniformly it works across the inputs). Technically, we formulate a representation-theoretical framework based on Schur-Weyl duality and permutation symmetry calculus that reduce the higher-moment Haar averages to a finite set of trace invariants of the composed correction unitaries. This yields closed-form expressions for FFF and DDD in arbitrary Hilbert-space dimension and delivers tight bounds that link the admissible deviation directly to the gap from the optimal average performance. In particular, any measured pair (F,D)(F, D)(F,D) can be ported into a visibility estimate for isotropic channel resources, turning the (F,D)(F, D)(F,D)-plane into a calibrated diagnostic map. We further cast the teleportation advantage and CGLMP-inequality violation as two witnesses lines in the (F,D)(F,D)(F,D) plane: one line certifies that FFF beats the classical benchmark 2/(d+1)2/(d{+}1)2/(d+1), while the other line certifies the Bell nonlocality. Their identical slope but distinct intercepts expose a quantitative gap between "entangled yet local" and "genuinely nonlocal" resources.
In this work, we introduce a comprehensive statistical framework for assessing single-qubit quantum teleportation performance beyond the conventional average-fidelity benchmark. At first, we derive a closed-form expression for the full probability density function of actual teleportation fidelities and apply it to both classical measure-and-prepare schemes and standard quantum teleportation, considering two relevant noise models: Bell-diagonal resource states and local amplitude-damping channels. These results reveal that protocols with identical average fidelities can exhibit markedly different statistical behaviors, and that relying solely on average fidelity can mask inherent asymmetries introduced by local noise, potentially leading to spurious conclusions of symmetry. Secondly, we introduce a certification method based on prior importance functions (e.g., Beta distributions), which unifies moment-based criteria and threshold-based success probabilities into a single figure of merit. Applying this framework, we show that certifying high-fidelity teleportation requires increasingly stronger entanglement or non-locality, and we clarify that the so-called ``fighting noise with noise'' effect arises from the chosen prior importance function rather than representing a genuine advantage. Our approach thus provides versatile tools for tailored, application-specific teleportation benchmarks.
Continuous-variable (CV) quantum teleportation is usually benchmarked by average fidelity, but when the teleportation is repeatedly used within optical networks or measurement-based architectures, uniformity across the input ensemble becomes equally important. We analyze this issue using two complementary figures of merit: the average fidelity and the fidelity deviation, which quantifies the input dependence of the single-shot teleportation fidelity. We prove that any deterministic unity-gain teleportation channel that is displacement covariant has vanishing fidelity deviation for coherent-state benchmarking, irrespective of whether the shared entangled resource is Gaussian or non-Gaussian. Nonzero deviation therefore diagnoses covariance breaking rather than non-Gaussianity. We then show that when a protocol raises the average fidelity through input-selective conditioning, the deviation generically increases in tandem, giving a quantitative universality cost. As a concrete example, we study teleportation enhanced by the so-called measurement-based noiseless linear amplification, where a heralded filter acts on the Bell-measurement record. The resulting trade-off among average fidelity, fidelity deviation, and success probability shows that stronger filtering can improve the conditional fidelity only by concentrating the successful events in favored regions of phase space, thereby suppressing the success probability and reducing input uniformity. Our results provide an operational framework for distinguishing genuine channel improvement from selectivity-driven post-selected advantage and suggest that the probabilistic CV teleportation should be assessed with average quality, universality, and heralding rate treated on an equal footing.
Abstract We analyze the performance of quantum teleportation in terms of average fidelity and fidelity deviation. The average fidelity is defined as the average value of the fidelities over all possible input states and the fidelity deviation is their standard deviation, which is referred to as a concept of fluctuation or universality. In the analysis, we find the condition to optimize both measures under a noisy quantum channel—we here consider the so-called Werner channel. To characterize our results, we introduce a 2D space defined by the aforementioned measures, in which the performance of the teleportation is represented as a point with the channel noise parameter. Through further analysis, we specify some regions drawn for different channel conditions, establishing the connection to the dissimilar contributions of the entanglement to the teleportation and the Bell inequality violation.
Quantum teleportation establishes a correspondence between an entangled state shared by two separate parties that can communicate classically and the presence of a quantum channel connecting the two parties. The standard benchmark for quantum teleportation, based on the average fidelity between the input and output states, indicates that some entangled states do not lead to channels which can be certified to be quantum. It was recently shown that if one considers a finer-grained witness, then all entangled states can be certified to produce a nonclassical teleportation channel. Here we experimentally demonstrate a complete characterization of a new family of such witnesses, of the type proposed in Phys. Rev. Lett. 119, 110501 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.110501 under different conditions of noise. We report nonclassical teleportation using quantum states that cannot achieve average fidelity of teleportation above the classical limit. We further use the violation of these witnesses to estimate the negativity of the shared state. Our results have fundamental implications in quantum information protocols and may also lead to new applications and quality certification of quantum technologies.
Quantum teleportation, a cornerstone of quantum information science, enables the transfer of an unknown quantum state from one location to another without physically moving the state itself. Its efficacy is primarily quantified by fidelity, a measure of how closely the teleported state resembles the original. Achieving high-fidelity teleportation is paramount for practical applications in quantum communication and computation. This paper explores the intricate relationship between non-locality, the no-cloning theorem, and the pursuit of high-fidelity quantum teleportation. We introduce the concept of "unclonable non-locality" to describe scenarios where the inherent non-local correlations of entangled states are leveraged in a manner that inherently resists illicit copying, thereby enhancing the integrity and security of the teleportation process. We review current state-of-the-art teleportation protocols, analyzing their fidelity limitations and the impact of various noise models, such as those arising from Bell-diagonal resource states and local amplitude-damping channels. Our framework emphasizes that protocols exhibiting identical average fidelities can conceal distinct statistical behaviors and asymmetries introduced by local noise, stressing the need for a comprehensive statistical assessment beyond simple average fidelity. We propose methods for constructing and utilizing entangled resources that maximize non-local correlations while inherently enforcing the no-cloning principle, thereby offering a robust pathway to deterministic, high-fidelity quantum state transfer. The discussion highlights the potential for designing tailored teleportation benchmarks based on prior importance functions, unifying moment-based criteria and threshold-based success probabilities into a single figure of merit, and clarifying the role of entanglement strength in certifying high-fidelity teleportation. We also acknowledge the ethical implications associated with the development of powerful quantum technologies that could have significant societal impacts.
Performance of quantum teleportation is typically measured by the average fidelity, an overlap between the input and output states. Along with the first moment, we introduce the second moment of fidelity in continuous-variable (CV) teleportation, i.e., the fidelity deviation as the figure of merit to assess the protocol's efficiency. We show that CV states, both Gaussian and non-Gaussian, can be better characterized by considering both average fidelity and fidelity deviation, which is not possible with only average fidelity. Moreover, we shed light on the performance of the teleportation protocol in two different input scenarios: One is when input states are sampled from constrained uniform distribution while the other one is Gaussian suppression of the input states which again leads to a different classification of CV states according to their performance. The entire analysis is carried out in noiseless and noisy scenarios with noise being incorporated in the measurement and the shared channels. We also report that one type of noise can make the protocol robust against the other one, which leads to a ``constructive effect,'' and identify the noise models which are responsible for decreasing average fidelity and the increment in fidelity deviation.